The Facebook app that runs in safe mode is a different (or should I say *should be the*) version that was pre-installed on the Note 2. If it's not, you can roll everything back to that version using the Application Manager.
Also, there are many config options for Facebook. It may be one of those that's causing the trouble. There are a ton of topics on Facebook in the Applications section of Android Forums that might help, though I'm a little surprised that Facebook doesn't have its own sub-forum there: it is popular enough, and enough of a troublemaker to warrant it.
For me, it's hot sunlight that's the problem. Sitting on my seat with the air conditioning on, but the sun beating down on it easily overheats (and freezes) my Note 2.